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Unitary Representations of Quantum Lorentz Group and Quantum Relativistic Toda Chain

M. A. Olshanetsky·V. -B. K. Rogov
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Abstract

The aim of this paper is to give a group theoretical interpretation of the three types of Bessel-Jackson functions. We consider a family of quantum Lorentz groups and a family of quantum Lobachevsky spaces. For three members of quantum Lobachevsky spaces the Casimir operators give rise to the two-body relativistic open Toda lattice Hamiltonians. Their eigen-functions are the modified Bessel-Jackson functions of three types. We construct the principal series of unitary irreducible representations of the quantum Lorentz groups. Special matrix elements in the irreducible spaces are the Bessel-Macdonald-Jackson functions. They are the wave functions of the two-body relativistic open Toda lattice. We obtain integral representations for these functions.

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BibTeXRIS

M. A. Olshanetsky, V. -B. K. Rogov. 2001-10-17. Unitary Representations of Quantum Lorentz Group and Quantum Relativistic Toda Chain. https://arxiv.org/abs/math/0110182

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